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2. While your algorithm is clearly efficient and can proveably help the most students, you begin to receive complaints from students that you didnt help (ie, their appointment was not part of the optimal solution). One of the students even offers to pay extra, which gives you a great idea. You w now allow students to make a donation to your favorite charity to make it more likely that their job will be selected. Let each appointment in this new set of appointments A be a triple (starti, endi, donation) of start and end times and donation amounts where end, > start, and donationui 0 You now need to update your algorithm to handle these donations along with the requested appointmen the amount of money you raise for your charity. t times. In this new environment, you are trying to maximize (a) (2 points) Give a specific case were your greedy algorithm would fail. (c) (3 points) Add memoization to this algorithm (d) (10 points) Give a bottom-up dynamic programming algorithm 2. While your algorithm is clearly efficient and can proveably help the most students, you begin to receive complaints from students that you didnt help (ie, their appointment was not part of the optimal solution). One of the students even offers to pay extra, which gives you a great idea. You w now allow students to make a donation to your favorite charity to make it more likely that their job will be selected. Let each appointment in this new set of appointments A be a triple (starti, endi, donation) of start and end times and donation amounts where end, > start, and donationui 0 You now need to update your algorithm to handle these donations along with the requested appointmen the amount of money you raise for your charity. t times. In this new environment, you are trying to maximize (a) (2 points) Give a specific case were your greedy algorithm would fail. (c) (3 points) Add memoization to this algorithm (d) (10 points) Give a bottom-up dynamic programming algorithm